The present invention relates to thiophene-sulfonic acid picolyl amides of the Formula (I), where RI to R7 and n are as defined in the claims and to the N-oxides, the agriculturally acceptable salts and the veterinarily acceptable salts of the compounds (I), with the proviso that if the thiophene ring is bonded to the sulfonyl group via position 2, R6 cannot be at position 5. The invention also relates to a process for preparing these compounds. Furthermore, the invention relates to the use of the compounds I and the N-oxides and the agriculturally acceptable salts thereof for combating phytopathogenic fungi (hereinafter referred to as harmful fungi). Additionally, the compounds (I), their N-oxides and salts can be used for controlling arthropodal pests. Furthermore, the invention relates to seed comprising a compound (I) or an N-oxide or agriculturally acceptable salt thereof.